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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image takes us once again to one of the infinity of fractals created by the formula Z^sqrt(2)+C, this time to the fractal that appears 1.4142 levels up the logarithmic ladder, a fractal that resembles a limbless torso with a head attached -- a perfect parent fractal for the day before Halloween. The scene is located in the chaos on the eastern side of the head. The image shows a small minibrot and its surrounding pattern. As must always be the case in fractals where the power of Z is fractional, the features in the image are broken and scrambled. But the broken features make a rough kind of symmetrical pattern around the midget, which is barely striking enough to raise the image to FOTD status. I can give no logical reason for the name "Square-Root Picnic". Since I have done so many of these scrambled fractals with exponents of Z between 1 and 2, and achieved only a modicum of success, I could not give the image an honest rating, but it is still worth a look. The calculation time of 7 minutes is slightly slow for such a less-than-splendid image. To save time and frustration, I recommend going to the FOTD web site at: After a foggy and frosty start, Monday turned quite pleasant here at Fractal Central, with sunny skies, light winds, and a high temperature of 55F 18C. The fractal cats were more concerned with something in the hallway than with the weather. They must still remember the mouse that popped out of the hole in the floor by the radiator last year around this time. When no mouse appeared on Monday, I comforted the disappointed duo with a treat of tuna and cheddar cheese. The next FOTD will appear in 24 hours. Until then, take care, and don't get caught up in a non-local fractal field pattern. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Square-Root_Picnic { ; time=0:07:06.50-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 logmap=848 periodicity=10
center-mag=-0.11106513807892870/+1.444879230159444\
/5.566726e+010/1/-52.5/0.0361740551652163 inside=0
params=1.4142/0/1.4142/0 float=y maxiter=3000
colors=000cAqcApcApcAncAmcAkcFkhKjmPhrUgvZgzcfzhdz\
mgzrdztczvaxt`vqZtpYsnXpkVnjTkgSjfRhdPfaOd`MaYL`XJ\
ZVIXSHVRFSOERMCOJBMI9LH8IE6HC5E93C82B6183062030020\
0100200300500600800900B00C00E00F00H00I00J00L10M10O\
10P10R11S11T11V21X21Y22Z22`22a22c33e33g33i33k33m35\
o35q55s55t56u56v56w56x28y36z56z65z85z95zB3zC3zE3zF\
2zH2zH2zI1zJ1zL1zM0zO0zP0zR0yS0xT0wT0vV0uX0tY0tZ0t\
`0ta0tc0td0tf0xd0tf0pg0mg0hh0fh1aj3Yj5Vk8Rm9OpCJqE\
FtHCvI8xL3xO5zM6zM8zM9xMBwMCvMEtMFsMHqMIsMJvMJxMLz\
MMzMOzMPzMRzMSzMTzMVyMXxMYwMZvRYuOYqMYmJYkIYiHYgEY\
eCYc9Ya8Y_6YY3YW2YU0YS0XQ0YO0YM0ZK0ZgzZqz`zz`zz`zz\
awzamzaczca0ca0c`0d`0d`0dZ0fZ0fY0zY0zg0zn0zn0zg0zV\
0zT0zT0zS0vS0nR0gR0`R0TP0FPgFOgFOgFMgFMgFMgFLgc9zc\
AzcEzcIzcMzcQzcUzcYzcazcezcizzmzzozzqzzszzuzzwzzyz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzwzzxzzzzzzzzzzzzzzz\
zzzzzzxzzwzzwzzvzztzztzzs }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*floor(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
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times.
